In some places you can hitchhike with your bike.

Beware, in many countries a lot of travel is by shared "Grande Taxis" (the french term as used in Africa). These travel more or less fixed routes. You may think you're hitch-hiking but you're not. You've flagged down someone who picks people up for a living, and there is a fixed fare for whatever journey it is you're doing. The fare is shared amongst the people on board. So the poor will wait for the vehicle to fill. You and I probably prefer not to wait, and prefer a vehicle that is not tightly packed.

However, anywhere that has a lot of pick-ups it's worth trying. If you're sharing with many others it will be cheap. Ecuador is supposed to be good.